Studying the bound state of the $B\bar{K}$ system in the Bethe-Salpeter formalism

In this work, we study the $B\bar{K}$ molecule in the Bethe-Salpeter (BS) equation approach. With the kernel containing one-particle-exchange diagrams and introducing two different form factors (monopole form factor and dipole form factor) in the vertex, we solve the BS equation numerically in the covariant instantaneous approximation. We investigate the isoscalar and isovector $B\bar{K}$ systems, and we find $X(5568)$ cannot be a $B\bar{K}$ molecule.